Q: A data set has $$Q_1 = 20$, Q_3$ = 40$$, and an IQR of 20. What is the lower fence for detecting outliers?

$$Q_1 - 1.5$$ \times IQR = 20 - 1.5 \times 20 = -10$$

Question 1

Which of the following statements best describes the relationship between the mean and median in a distribution that is skewed right?

Accepted Answer

The mean is substantially larger than the median.

Question 2

Given the following data set: 12, 15, 14, 10, 18, 20, 13. What is the median?

Accepted Answer

$$14$$

Question 3

Which measure of central tendency is most appropriate to use when a data set contains extreme outliers?

Accepted Answer

Median

Question 4

A sample of three travel times (in minutes) is: 5, 26, 36. Calculate the sample standard deviation $$s.$$

Accepted Answer

$$s = \sqrt{\frac{(5-22.333)^2$ + (26-22.333)^2$ + (36-22.333)^2$}{2}} \approx 15.82$$

Question 5

If a distribution is symmetric, which of the following is true?

Accepted Answer

Mean is roughly equal to the median.

Question 6

The Empirical Rule states that for a bell-shaped distribution, approximately what percentage of data falls within two standard deviations of the mean?

Accepted Answer

$$95\%$$

Question 7

Given the data set: 5, 8, 12, 15, 18, 22, 25, what is the range?

Accepted Answer

$$25 - 5 = 20$$

Question 8

Which of the following formulas correctly calculates the population standard deviation $$\sigma$$ for $$N$$ observations $$x_1$$, $$x_2$$, ..., x_N$$ with mean $$\mu$$?

Accepted Answer

$$\sigma = \sqrt{\frac{\sum (x_i - \mu)^2$}{N}}$$

Question 9

A student scored 85 on a test where the mean was 75 and the standard deviation was 5. What is the student's z-score?

Accepted Answer

$$z = \frac{85 - 75}{5} = 2$$

Question 10

Which of the following best describes the interquartile range (IQR)?

Accepted Answer

The difference between the third quartile and the first quartile: $$IQR = Q_3$ - Q_1$

Question 11

A boxplot is constructed for two different restaurants' wait times. Restaurant A's box is much wider than Restaurant B's. What does this indicate?

Accepted Answer

Restaurant A has more variability in wait times.

Question 12

Which of the following is NOT a resistant measure of central tendency?

Accepted Answer

Mean

Question 13

If a data set has no repeated values, what can be said about its mode?

Accepted Answer

The data set has no mode.

Question 14

A data set has $$Q_1 = 20$, Q_3$ = 40$$, and an IQR of 20. What is the lower fence for detecting outliers?

Accepted Answer

$$Q_1 - 1.5$$ 	imes IQR = 20 - 1.5 	imes 20 = -10$$

Question 15

Which of the following best describes the five-number summary?

Accepted Answer

Minimum, $$Q_1$$, Median, $$Q_3$$, Maximum

Question 16

If a distribution is skewed left, which measure of central tendency is preferred for describing the center?

Accepted Answer

Median

Question 17

A data set has a mean of 50 and a standard deviation of 5. According to the Empirical Rule, approximately what percentage of data falls between 45 and 55?

Accepted Answer

$$68\%$$

Question 18

Which formula is used to calculate the sample variance $$s^2$$ for $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$ with mean $$\bar{x}$$?

Accepted Answer

$$s^2$$ = \frac{\sum (x_i - \bar{x}$$)^2$$}{n-1}$$

Question 19

A student’s test score is at the 90th percentile. What does this mean?

Accepted Answer

The student scored higher than 90% of the students.

Question 20

Which of the following is true about the mode?

Accepted Answer

It is the value that occurs most frequently in the data set.

Chapter 3 STATS

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